Luttinger theorem and low energy properties of ideal Haldane-Sutherland Liquids

We study in this paper the properties of a many body system of fermions obeying exclusion-statistics (Haldane liquid) where the origin of exclusion statistics is coming from an interaction-induced displacement field ${\mathbf{a}}_{\mathbf{k}}$ introduced by Sutherland (Haldane-Sutherland liquid). In particular we show how the Luttinger Theorem becomes compatible with exclusion statistics as a result of momentum conservation and adiabaticity. As a result, the low energy properties of Haldane-Sutherland liquids are Fermi/Luttinger liquid-like.